# Analytical Radiation Transport Benchmarks for The Next Century

## Abstract

Verification of large-scale computational algorithms used in nuclear engineering and radiological applications is an essential element of reliable code performance. For this reason, the development of a suite of multidimensional semi-analytical benchmarks has been undertaken to provide independent verification of proper operation of codes dealing with the transport of neutral particles. The benchmarks considered cover several one-dimensional, multidimensional, monoenergetic and multigroup, fixed source and critical transport scenarios. The first approach, called the Green's Function. In slab geometry, the Green's function is incorporated into a set of integral equations for the boundary fluxes. Through a numerical Fourier transform inversion and subsequent matrix inversion for the boundary fluxes, a semi-analytical benchmark emerges. Multidimensional solutions in a variety of infinite media are also based on the slab Green's function. In a second approach, a new converged SN method is developed. In this method, the SN solution is ''minded'' to bring out hidden high quality solutions. For this case multigroup fixed source and criticality transport problems are considered. Remarkably accurate solutions can be obtained with this new method called the Multigroup Converged SN (MGCSN) method as will be demonstrated.

- Authors:

- Publication Date:

- Research Org.:
- University of Arizona (US)

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 836281

- Report Number(s):
- DOE/ID/14113

TRN: US0500548

- DOE Contract Number:
- FG07-01ID14113

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 19 Jan 2005

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; BENCHMARKS; CRITICALITY; DISCRETE ORDINATE METHOD; GEOMETRY; INTEGRAL EQUATIONS; NEUTRAL PARTICLES; NUCLEAR ENGINEERING; PERFORMANCE; RADIATION TRANSPORT; TRANSPORT; VERIFICATION

### Citation Formats

```
Ganapol, B D.
```*Analytical Radiation Transport Benchmarks for The Next Century*. United States: N. p., 2005.
Web. doi:10.2172/836281.

```
Ganapol, B D.
```*Analytical Radiation Transport Benchmarks for The Next Century*. United States. doi:10.2172/836281.

```
Ganapol, B D. Wed .
"Analytical Radiation Transport Benchmarks for The Next Century". United States. doi:10.2172/836281. https://www.osti.gov/servlets/purl/836281.
```

```
@article{osti_836281,
```

title = {Analytical Radiation Transport Benchmarks for The Next Century},

author = {Ganapol, B D},

abstractNote = {Verification of large-scale computational algorithms used in nuclear engineering and radiological applications is an essential element of reliable code performance. For this reason, the development of a suite of multidimensional semi-analytical benchmarks has been undertaken to provide independent verification of proper operation of codes dealing with the transport of neutral particles. The benchmarks considered cover several one-dimensional, multidimensional, monoenergetic and multigroup, fixed source and critical transport scenarios. The first approach, called the Green's Function. In slab geometry, the Green's function is incorporated into a set of integral equations for the boundary fluxes. Through a numerical Fourier transform inversion and subsequent matrix inversion for the boundary fluxes, a semi-analytical benchmark emerges. Multidimensional solutions in a variety of infinite media are also based on the slab Green's function. In a second approach, a new converged SN method is developed. In this method, the SN solution is ''minded'' to bring out hidden high quality solutions. For this case multigroup fixed source and criticality transport problems are considered. Remarkably accurate solutions can be obtained with this new method called the Multigroup Converged SN (MGCSN) method as will be demonstrated.},

doi = {10.2172/836281},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2005},

month = {1}

}